Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
arXiv:2304.06677 · doi:10.1007/JHEP08(2023)141
Abstract
A correspondence is established between the dynamics of the two-vortex system and the non-commutative Landau problem (NCLP) in its sub- (non-chiral), super- (chiral) and critical phases. As a result, a trivial permutation symmetry of the point vortices induces a weak-strong coupling duality in the NCLP. We show that quantum two-vortex systems with non-zero total vorticity can be generated by applying conformal bridge transformation to a two-dimensional quantum free particle or to a quantum vortex-antivortex system of zero total vorticity. The sub- and super-critical phases of the quantum NCLP are generated in a similar way from the 2D quantum free particle in a commutative or non-commutative plane. The composition of the inverse and direct transformations of the conformal bridge also makes it possible to link the non-chiral and chiral phases in each of these two systems.
arXiv comment30 pages
References in corpus (38)
- Gauge Theory Correlators from Non-Critical String Theory
- Non-Abelian Anyons and Topological Quantum Computation
- Large N Field Theories, String Theory and Gravity
- Comments on the Sachdev-Ye-Kitaev model
- Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
- Gravity duals for non-relativistic CFTs
- Non-Commutative Quantum Mechanics
- Quantum mechanics on the noncommutative plane and sphere
- The exotic Galilei group and the "Peierls substitution"
- Solving the Schwarzian via the Conformal Bootstrap
- Exotic galilean symmetry in the non-commutative plane, and the Hall effect
- Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
- The non-commutative Landau problem
- Conformal quantum mechanics as the CFT dual to AdS
- On the spectrum of nonrelativistic AdS/CFT
- Anyon wave equations and the noncommutative plane
- Spectrum of Schroedinger field in a noncommutative magnetic monopole
- Anyon spin and the exotic central extension of the planar Galilei group
- Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
- Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
- Conformal Symmetry of Relativistic and Nonrelativistic Systems and AdS/CFT Correspondence
- Nonrelativistic anyons in external electromagnetic field
- -symmetric invisible defects and confluent Darboux-Crum transformations
- Coupling constant metamorphosis and Nth order symmetries in classical and quantum mechanics
- Chiral asymmetry in propagation of soliton defects in crystalline backgrounds
- Conformal bridge between asymptotic freedom and confinement
- Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
- Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane
- Super-extended noncommutative Landau problem and conformal symmetry
- Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background
- Conformal generation of an exotic rotationally invariant harmonic oscillator
- Hidden symmetry and (super)conformal mechanics in a monopole background
- Quantum dynamics of two-dimensional vortex pairs with arbitrary total vorticity
- Noncommutative mechanics, Landau levels, twistors and Yang-Mills amplitudes
- Non-commuting coordinates in vortex dynamics and in the Hall effect, related to "exotic" Galilean symmetry
- Generalised point vortices on a plane
- Conformal bridge in a cosmic string background
- Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane